The youngster suffered “superficial” injuries after being struck by the small black vehicle in the grounds of Lidl, off Longridge Road, Whitburn, at around 6.20pm.
A man who was driving the car stopped to check that the child was alright, however he did not remain at the scene. Police are appealing for him to come forward.
The victim was taken to St John’s hospital to be checked over.
Roads Policing Inspector Richard Latto said: “While the driver initially stopped to check on the welfare of the child, we are keen to speak to him so we can continue our enquiries.
“Anyone with information regarding this incident is asked to contact the police.”
Those with information can contact Police Scotland on 101 or anonymously through Crimestoppers on 0800 555 111.